We suppress notation and omit the \(G\)  when it is clear from the context. It is clear that each map \(m := (D,R,E)\) , where \(R \in \mathcal {R}, E \in \mathcal {E}\)  gives an embedding of \(G\) , see [1]} [2]} for details. In fact, the set \(\lbrace  (D,R,E) : R \in \mathcal {R} \rbrace \)  (where we fix any edge scheme) is in bijection with the set of all embeddings of \(G\)  given by local rotations. Therefore each possible embedding of \(G\)  appears \(| \mathcal {E} |\)  times in \(\lbrace  (D,R,E) : R \in \mathcal {R}, E \in \mathcal {E} \rbrace \) . We choose to study this set where we vary the edge scheme instead of fixing \(E\) , as it will prove convenient in our analysis. This explains the following observation:
